Generalized Minimax-Concave Regularization for Aero-engine Fan Acoustic Mode Measurements

Acoustic mode investigation provides essential guidance in silent aero-engine designing by measuring pressure perturbations around the duct. Instead of mounting a full sensor array (FSA), compressive sampling (CS) feasibly achieves identical resolution with lower microphone requirement. In this paper, a generalized minimax-concave (GMC) regularized CS model is proposed as alternative to L1-norm regularized one for acoustic mode measurements, offering more accurate results by the use of fewer microphones. Improvement is guaranteed by the potential of GMC penalty due to sparsity inducing. Meanwhile the convexity of the cost function is also maintained via setting the scale matrix. It captures both advantages of nonconvex regularization and convex optimization. The effectiveness of the approach is validated on an aero-engine fan test rig. The tonal noise series are firstly separated from the sound pressure signals via cyclostationary analysis, thus amplitudes of tonal modes are estimated exactly. Two cases under different shaft speeds are conducted to estimate acoustic tonal modes, and results indicate that the proposed approach outperforms L1-norm regularized method in reconstruction accuracy. The effect of sensor number on reconstruction accuracy is also investigated, showing the proposed GMC method enables appropriate mode estimation from much fewer sensors.